Measurement of Strange Quark Contributions to the
Vector Form Factors of the Proton at Q[superscript
2]=0.22(GeV/c)[superscript 2]
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Baunack, S. et al "Measurement of Strange Quark Contributions
to the Vector Form Factors of the Proton at Q2=0.22 (GeV/c)2."
Physical Review Letters 102.15 (2009): 151803. © 2009 The
American Physical Society
As Published
http://dx.doi.org/10.1103/PhysRevLett.102.151803
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Detailed Terms
PRL 102, 151803 (2009)
week ending
17 APRIL 2009
PHYSICAL REVIEW LETTERS
Measurement of Strange Quark Contributions to the Vector Form Factors
of the Proton at Q2 ¼ 0:22 ðGeV=cÞ2
S. Baunack,1,* K. Aulenbacher,1 D. Balaguer Rı́os,1 L. Capozza,1 J. Diefenbach,1 B. Gläser,1 D. von Harrach,1 Y. Imai,1
E.-M. Kabuß,1 R. Kothe,1 J. H. Lee,1 H. Merkel,1 M. C. Mora Espı́,1 U. Müller,1 E. Schilling,1 G. Stephan,1 C. Weinrich,1
J. Arvieux,2,† M. A. El-Yakoubi,2 R. Frascaria,2 R. Kunne,2 F. E. Maas,2,‡ M. Morlet,2 S. Ong,2 J. van de Wiele,2
S. Kowalski,3 Y. Prok,3 and S. Taylor3
1
Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, J.J. Becherweg 45, D-55099 Mainz, Germany
2
Institut de Physique Nucléaire, CNRS-IN2P3, Université Paris-Sud, F-91406 Orsay Cedex, France
3
Laboratory for Nuclear Science and Department of Physics, MIT, Cambridge, Massachusetts 02139, USA
(Received 17 November 2008; published 16 April 2009)
A new measurement of the parity violating asymmetry in elastic electron scattering on hydrogen at
backward angles and at a four momentum transfer of Q2 ¼ 0:22 ðGeV=cÞ2 is reported here. The measured
asymmetry is ALR ¼ ð17:23 0:82stat 0:89syst Þ 106 . The standard model prediction assuming no
strangeness is A0 ¼ ð15:87 1:22Þ 106 . In combination with previous results from measurements at
forward angles, it is possible to disentangle for the first time the strange form factors at this momentum
transfer, GsE ¼ 0:050 0:038 0:019 and GsM ¼ 0:14 0:11 0:11.
DOI: 10.1103/PhysRevLett.102.151803
PACS numbers: 13.40.Gp, 11.30.Er, 12.15.y, 14.20.Dh
Sea quarks are an important ingredient to describe nucleon properties in terms of fundamental QCD degrees of
freedom. Strange quark-antiquark pairs might play a relevant role and affect, e.g., the electromagnetic properties of
the nucleon. The contribution of strange quarks to the
charge radius and magnetic moment in the nucleon ground
state is of specific interest since this is a pure sea quark
effect. The strange quark contribution to the electromagnetic form factors of the nucleon can be expressed in terms
of the strange electric and magnetic form factors GsE and
GsM . There are various theoretical approaches for estimating the strange form factors [1,2], such as quark soliton
models [3–5], chiral quark models [6], quenched lattice
calculations [7], or two-component models [8]. Parity violating electron scattering provides a direct experimental
approach [9–11].
A measurement of parity violation necessarily involves a
weak interaction probe of the nucleon. This provides additional information allowing a measurement of GsE and GsM .
Within the standard model of electroweak interaction, it is
known that electromagnetic and weak currents are related.
Assuming isospin symmetry, the weak vector form factors
~ pE;M of the proton, describing the vector coupling to the Z0
G
boson, can be expressed in terms of the electromagnetic
nucleon form factors Gp;n
E;M and the strange form factors
GsE;M . The interference between tree level electromagnetic
and weak amplitudes leads to a parity violating asymmetry
in the elastic scattering cross section of left- and righthanded electrons (LR) L , R : ALR ¼ ðR L Þ=ðR þ
L Þ. This asymmetry can be written as a sum of three
terms, ALR ¼ AV þ AS þ AA . AV represents the vector
coupling on the proton vertex without strangeness contribution, AS contains the strange quark vector contribution, and AA represents the axial coupling to the proton
0031-9007=09=102(15)=151803(4)
vertex [11]:
Gp Gn þ GpM GnM
AV ¼ a0eq ð1 4^ 0eq s^2Z Þ E p E2
; (1)
ðGE Þ þ ðGpM Þ2
AS ¼ a0eq
GpE GsE þ GpM GsM
;
ðGpE Þ2 þ ðGpM Þ2
pffiffiffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
~p
ð1 4s^2Z Þ 1 2 ð1 þ ÞGpM G
A
AA ¼ a
;
ðGpE Þ2 þ ðGpM Þ2
(2)
(3)
G Q2
pffiffi , G the Fermi coupling constant, the
with a ¼ 4
2
fine structure constant, ¼ Q2 =ð4Mp2 Þ, Q2 the negative
squared four momentum transfer, Mp the proton mass,
and ¼ ½1 þ 2ð1 þ Þtan2 21 . is the scattering angle
in the laboratory frame and s^2Z ðMZ Þ ¼ 0:231 19ð14Þ [12] is
the square of the sine of the weak-mixing angle. The
factors 0eq and ^ 0eq include the electroweak radiative corrections evaluated in the minimal subtraction renormalization scheme (MS). The electromagnetic form factors Gp;n
E;M
are taken from a Monte Carlo based analysis of the world
data [13] resulting in the nonstrangeness expectation A0 ¼
AV þ AA ¼ ð15:87 1:22Þ 106 . The dominant contribution to the uncertainty of A0 comes from the uncertainty due to the two-quark radiative corrections (anapole
~p , followed by the
moment) in the axial form factor G
A
p
n
uncertainties in GM and GM .
Recently four groups have published related results. The
SAMPLE Collaboration at MIT-Bates [14,15] involved a
backward angle measurement on a hydrogen target at a
four momentum transfer of Q2 ¼ 0:1 ðGeV=cÞ2 and on
deuterium at Q2 ¼ 0:1 ðGeV=cÞ2 and 0:04 ðGeV=cÞ2 ,
~p . The HAPPEX
being sensitive mainly to GsM and G
A
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Ó 2009 The American Physical Society
PRL 102, 151803 (2009)
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PHYSICAL REVIEW LETTERS
TABLE I. Average beam parameters X i of the electron beam and the associated false
asymmetries ai X i .
i
1
2
3
4
5
6
ai Xi
X i
Parameter
0:30 ppm
86:97 nm
23:84 nm
8:53 nrad
2:40 nrad
0:41 eV
Current asymmetry
Horizontal position differences
Vertical position differences
Horizontal angle differences
Vertical angle differences
Energy differences
Collaboration at TJNAF reported a measurement on a
hydrogen target at forward angles at a Q2 of
0:47 ðGeV=cÞ2 , mainly sensitive to GsE [16] and a precise
measurement with helium and proton targets at a Q2 of
0:1 ðGeV=cÞ2 [17]. Those measurements put tight constraints on the strangeness contribution to the form factors
at these momentum transfers. The G0 Collaboration at
TJNAF performed a forward angle measurement with
several momentum transfers between 0:1 ðGeV=cÞ2 and
1 ðGeV=cÞ2 , including the momentum transfer discussed
here [18]. The A4 Collaboration at MAMI has completed
measurements on a hydrogen target at forward angles and
momentum transfers of 0:23 ðGeV=cÞ2 and 0:1 ðGeV=cÞ2
[19,20]. They were sensitive mainly to GsE . Here, a new
measurement of the parity violating asymmetry in the
elastic scattering of polarized electrons off unpolarized
protons at backward angles at Q2 ¼ 0:22 ðGeV=cÞ2 is
presented and the implications of the new result for the
strange form factors are discussed. A single measurement
of AS gives a linear combination of GsE and GsM . Two
measurements with the same momentum transfer but
with different scattering angles allow the separation of
~ p is taken as an input
the two strange form factors when G
A
parameter. With the A4 experimental setup [19,21] at the
MAMI accelerator [22] scattering angles either between
30 and 40 or 140 and 150 are possible. As Q2 ¼
41 E2 sin2 ð=2Þ, where ¼ 1 þ E=Mp ð1 cosÞ, the
momentum transfer can be selected by varying the beam
energy E. To match the Q2 value of the A4 forward
measurement a beam energy of 315.1 MeV was chosen
for the backward angle experiment.
The experimental setup was described in detail in [19].
Here we summarize the basic components and emphasize
the modifications that have been made. A superlattice
photocathode delivered a polarized electron beam with
an intensity of 20 A and an average polarization Pe of
about 70%. The beam polarization was measured once a
week using a Møller polarimeter with a precision of 2%. In
addition, a Mott and a transmission Compton polarimeter
were used. Altogether, the uncertainty to the beam polarization is 4%. It was important to minimize helicity correlated beam fluctuations in position, angle, current, and
energy that introduce false asymmetries due to changes
in luminosity, cross section, or solid angle. Table I lists the
measured beam parameters during the 1100 h of asymme-
0:25
þ0:61
0:86
0:09
þ0:10
þ0:16
ppm
ppm
ppm
ppm
ppm
ppm
try data taking. The liquid hydrogen target [23] was
23.4 cm long yielding a luminosity L 1:2 1038 cm2 s1 . Target density fluctuations were monitored
by Cherenkov luminosity monitors located at small scattering angles [24] and were kept below L=L < 106
averaged over the whole data set. The scattered electrons
were detected in a homogenous electromagnetic calorimeter that consists of 1022 lead fluoride (PbF2 ) crystals [25]
as single
pffiffiffiffi events achieving an energy resolution of about
3:9%= E. The detector covered a solid angle of ¼
0:62 sr.
The most important aspect of the backward measurement is the installation of 72 plastic scintillators in front of
the PbF2 crystals (see Fig. 1). Used in coincidence with the
calorimeter, they enable the separation of charged from
neutral particles. Photons from 0 decay could thus be
separated from scattered electrons. The energy that was
deposited by a particle in the calorimeter was digitized by
an 8 bit ADC and stored into a coincidence or a noncoincidence histogram depending on the trigger signal
2
2
FIG. 1. Drawing of the PbF2 calorimeter. The scintillators are
placed between the scattering chamber and the lead fluoride
crystals. The system is mounted on a rotatable platform.
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PRL 102, 151803 (2009)
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PHYSICAL REVIEW LETTERS
from the scintillator. Furthermore a polarization signal
distinguished between the two helicity states of the
beam. Altogether each calorimeter channel produced four
histograms for each 5 min data taking run.
The data analysis was similar to that of the previous
measurements [20]. Modifications were needed since the
coincidence histograms were polluted by high energy photons converting into eþ e pairs in the aluminum wall of
the vacuum chamber and in the scintillator. The
LR asymmetry of the background was determined
from the noncoincidence spectra. A detailed Monte Carlo
simulation using GEANT4 was implemented for tracking
shower particles and calculating the detector response.
The simulation reproduced the measured spectrum well
for energies above 125 MeV, while for lower energies
threshold effects of the analogue readout electronics become important. From the simulation one can derive as a
function of the energy both the probability of a to
convert and trigger the scintillator and the mean energy
loss of the generated eþ e pairs. Figure 2 shows the
measured energy spectra and the contributions from the
different processes. The contribution to the background
arising from aluminum events from the target entrance
and exit windows was determined by a measurement
with an empty target and is about 4.5%. The background
elimination was achieved by scaling the measured noncoincidence spectra with the conversion probability and
shifting them by the energy loss. Different methods for this
procedure were applied and gave differences in the final
asymmetry below 0:2 106 .
The number of elastic events for the two helicities was
determined by applying cuts on the coincidence energy
histograms as indicated in Fig. 2 by the dotted lines and
summing up all 730 channels of the inner five calorimeter
rings. For each run the raw asymmetry is calculated. The
false asymmetries are corrected using the ansatz Araw ¼
P
Aexpt þ 6i¼1 ai Xi , where the Xi denote the helicity correlated beam parameters as defined in Table I. The ai denote
the correlation coefficients between the observed asymmetry Araw and the beam parameters Xi . These coefficients
have been determined from geometry and in addition from
the intrinsic beam fluctuations via a multiple linear regression analysis. Both methods yield only small corrections
relative to the measured asymmetry and agree within the
statistical precision. Finally the physical asymmetry ALR is
obtained by normalization of Aexpt by the electron beam
polarization Pe : ALR ¼ Aexpt =Pe . About half of our data
was taken with a half-wave plate inserted in the laser optics
of the electron source. This leads to a reversal of the beam
helicity and a partial compensation of helicity correlated
false asymmetries. All relevant corrections applied to the
measured asymmetry are listed in Table II. The asymmetry
for the aluminum events is calculated in the static approximation. Another source of background is accidental coincidence events in the scintillators with a fraction of about
1.3%. Since the event rate on the detector is 4–8 times
smaller than in our forward measurements, corrections on
the asymmetry due to pileup are negligible here. Figure 3
shows the parity violating asymmetries for the whole data
set. The sign flip when the half-wave plate was inserted can
be clearly observed. In total 3 1012 coincidence events
were used for the full analysis. An asymmetry of ALR ¼
ð17:23 0:82stat 0:89syst Þ 106 is extracted.
From the difference between ALR and A0 the linear
combination of the strange electric and magnetic form
factors GsM þ 0:26GsE ¼ 0:12 0:11 0:11 is obtained,
where the first error comes from the measurement and the
FIG. 2. Left panel: The measured energy spectrum of coincidence events is shown by the dashed line. One can clearly
identify the peak of the elastic scattered electrons. The contributions of the different processes are shown from bright to dark:
(i) the elastically scattered electrons, (ii) the inelastically scattered electrons, (iii) the converted photons from 0 decay, and
(iv) empty target background. Upper right panel: The solid line
shows a measured energy spectrum of noncoincidence events.
Lower right panel: The dotted line shows the background contribution to the coincidence spectrum estimated from the noncoincidence events by applying the shifting and scaling method
in comparison with the photon background obtained from the
simulation (gray) together with the shifted and scaled noncoincidence events from an empty target measurement (dark).
TABLE II. Applied corrections to the measured asymmetry
and their contribution to the systematic error.
Applied scaling factor
Scaling factor
Error
0.683
0.040
Polarization Pe
Applied corrections
Helicity correlated beam differences
Accidental coincidence events
Al windows (H2 target)
Dilution of 0 decay photons
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Correction
(ppm)
Error
(ppm)
0.14
0:19
0.29
1:49
0.39
0.02
0.04
0.28
PRL 102, 151803 (2009)
Asymmetries (ppm)
PHYSICAL REVIEW LETTERS
in
out
in
out
in
out
in
out out
in
out
in
out out
in
Data Set Number
FIG. 3. Measured asymmetries ALR with respect to the position
of the half-wave plate at the electron source (in or out). The
reversal of the helicity can be easily observed in the sign flip of
the extracted asymmetries. The two gray bands show fits to the
data, Aout ¼ ð17:70 1:27Þ ppm and Ain ¼ ð16:68 1:37Þ ppm (omitting systematic errors).
second from the uncertainty in the axial and electromagnetic form factors of the nucleon. In Fig. 4 the shaded band
shows the possible values of GsE and GsM within the
one- uncertainty. The hatched band shows the A4 result
of the forward angle measurement at the same momentum
transfer. Because of a careful reanalysis of the electron
polarization measurement and using an up-to-date parametrization of the electromagnetic form factors [13], the value
of the linear combination has shifted down from GsE þ
0:225GsM ¼ 0:039 0:028 0:020 as presented in [19]
to GsE þ 0:224GsM ¼ 0:020 0:029 0:016. Disentangling the linear combinations, one gets GsE ¼ 0:050 0:038 0:019 and GsM ¼ 0:14 0:11 0:11. Including the G0 forward angle measurement at Q2 ¼
0:23 ðGeV=cÞ2 one gets a more precise value of GsE ¼
FIG. 4. The linear combination of GsE þ GsM from this work
(solid band) together with the A4 forward angle measurement
[19] (hatched band). The bands represent the possible values of
GsE þ GsM within the one- uncertainty with statistical and
systematic error added in quadrature. The ellipses show the
68% and 95% C.L. constraints in the GsE -GsM plane. Also shown
are theoretical predictions [3,5–8].
week ending
17 APRIL 2009
0:035 0:030 0:019. The strange form factors presented here are determined simultaneously from two complementary A4 measurements with the same momentum
transfer using the same method. In contrast to the only
existing published backward angle measurement at a lower
Q2 of 0:1 ðGeV=cÞ2 favoring a positive value of GsM [14],
the new result favors a negative strange magnetic moment as predicted by many models and also in accordance
with the latest lattice calculation [7]. Furthermore, it disfavors a negative GsE in this momentum transfer region as
suggested by [18]. Both HAPPEX and A4 Collaborations
have scheduled measurements in the near future to clarify
the situation for GsE at Q2 ¼ 0:6 ðGeV=cÞ2 .
*Corresponding author.
baunack@kph.uni-mainz.de
†
Deceased.
‡
Present address: Gesellschaft für Schwerionenforschung
Darmstadt and Johannes Gutenberg-Universität Mainz,
Germany.
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